Found 634 Documents (Results 1–100)
\(RLL\)-realization of two-parameter quantum affine algebra in type \(D_n^{(1)}\). (English) Zbl 07877908
Reviewer: Yang Shilin (Beijing)
Supersymmetric generalization of \(q\)-deformed long-range spin chains of Haldane-Shastry type and trigonometric \(\mathrm{GL}(N|M)\) solution of associative Yang-Baxter equation. (English) Zbl 07834704
\(t\)-quantized Cartan matrix and R-matrices for cuspidal modules over quiver Hecke algebras. (English) Zbl 07823123
\(R\)-matrix for the 8-dimensional spin representation of \(U_q (\mathfrak{so}_7)\). (English) Zbl 07806020
Cluster variables for affine Lie-Poisson systems. (English. Russian original) Zbl 07824560
Theor. Math. Phys. 217, No. 3, 1987-2004 (2023); translation from Teor. Mat. Fiz. 217, No. 3, 672-693 (2023).
\(R\)-matrix presentation of quantum affine algebra in type \(A_{2n-1}^{(2)}\). (English) Zbl 1537.17025
Reviewer: Yang Shilin (Beijing)
MSC:
17B37
Shapovalov elements and Hasse diagrams. (English. Russian original) Zbl 1521.17027
Theor. Math. Phys. 216, No. 3, 1255-1264 (2023); translation from Teor. Mat. Fiz. 216, No. 3, 405-416 (2023).
Higher-rank generalization of the 11-vertex rational \(R\)-matrix: IRF-vertex relations and the associative Yang-Baxter equation. (English. Russian original) Zbl 1521.81114
Theor. Math. Phys. 216, No. 2, 1083-1103 (2023); translation from Teor. Mat. Fiz. 216, No. 2, 203-225 (2023).
Affinization of \(q\)-oscillator representations of \(U_q (\mathfrak{gl}_n)\). (English) Zbl 1528.17010
Yang-Baxter deformation of WZW model based on Lie supergroups: the cases of \(GL(1|1)\) and \((C^3 + A)\). (English) Zbl 1519.81445
The \(R\)-matrix of the quantum toroidal algebra. (English) Zbl 1534.17018
Reviewer: Istvan Heckenberger (Marburg)
MSC:
17B37
Poles of finite-dimensional representations of Yangians. (English) Zbl 1530.17015
Reviewer: Sorin Dascalescu (Bucureşti)
Automorphic symmetries and \(AdS_n\) integrable deformations. (English) Zbl 07819675
Dobrev, Vladimir (ed.), Lie theory and its applications in physics. Selected papers based on the presentations at the workshop, Sofia, Bulgaria, online, June 2021. Singapore: Springer. Springer Proc. Math. Stat. 396, 351-358 (2022).
Roots of the characteristic equation for the symplectic groupoid. (English. Russian original) Zbl 1527.15011
Russ. Math. Surv. 77, No. 3, 552-554 (2022); translation from Usp. Mat. Nauk 77, No. 3, 177-178 (2022).
On the \(R\)-matrix identities related to elliptic anisotropic spin Ruijsenaars-Macdonald operators. (English. Russian original) Zbl 1516.81107
Theor. Math. Phys. 213, No. 2, 1543-1559 (2022); translation from Teor. Mat. Fiz. 213, No. 2, 268-286 (2022).
Quasitriangular structures on the super-Yangian and quantum loop superalgebra, and difference equations. (English. Russian original) Zbl 1516.17016
Theor. Math. Phys. 213, No. 1, 1423-1440 (2022); translation from Teor. Mat. Fiz. 213, No. 1, 129-148 (2022).
The generalized Lipkin-Meshkov-Glick model and the modified algebraic Bethe ansatz. (English) Zbl 1513.81079
Coherent categorical structures for Lie bialgebras, Manin triples, classical \(r\)-matrices and pre-Lie algebras. (English) Zbl 1500.17021
Reviewer: Alexander B. Levin (Washington)
Stable maps, \(Q\)-operators and category \(\mathcal{O}\). (English) Zbl 1502.17013
Reviewer: Yang Shilin (Beijing)
Explicit R-matrices for inhomogeneous 3D chiral Potts models: integrability and the action formulation for IM. (English) Zbl 1484.81109
Graded quiver varieties and singularities of normalized R-matrices for fundamental modules. (English) Zbl 1512.17021
Reviewer: Mee Seong Im (Annapolis)
Polynomial structure of Gromov-Witten potential of quintic \(3\)-folds. (English) Zbl 1478.14084
Reviewer: Sergiy Koshkin (Houston)
A variational \(R\)-matrix finite element procedure for solving ultra-cold collision problems. (English) Zbl 1476.65300
Quadratic algebras based on \(SL(NM)\) elliptic quantum \(R\)-matrices. (English. Russian original) Zbl 1471.81051
Theor. Math. Phys. 208, No. 2, 1156-1164 (2021); translation from Teor. Mat. Fiz. 208, No. 2, 355-364 (2021).
The \(R\)-matrix of the quantum toroidal algebra \(U_{q,t}(\overset{..}{gl}_1)\) in the Fock module. (English) Zbl 1476.17006
Reviewer: Stepan Moskaliuk (Kyiv)
Yangians versus minimal \(W\)-algebras: a surprising coincidence. (English) Zbl 1496.17011
Reviewer: Andrea Appel (Parma)
RMT: \(R\)-matrix with time-dependence. Solving the semi-relativistic, time-dependent Schrödinger equation for general, multielectron atoms and molecules in intense, ultrashort, arbitrarily polarized laser pulses. (English) Zbl 07678513
UKRmol+: a suite for modelling electronic processes in molecules interacting with electrons, positrons and photons using the R-matrix method. (English) Zbl 07678498
Revisiting the Askey-Wilson algebra with the universal \(R\)-matrix of \(U_q(\mathfrak{sl}_2)\). (English) Zbl 1511.17029
Introduction to the algebraic Bethe ansatz. (English) Zbl 1483.82003
Kielanowski, Piotr (ed.) et al., Geometric methods in physics XXXVIII. Workshop, Białowieża, Poland, June 30 – July 6, 2019. Cham: Birkhäuser. Trends Math., 363-371 (2020).
Reviewer: Takeo Kojima (Yonezawa)
Quantization of a Poisson structure on products of principal affine spaces. (English) Zbl 1485.53107
Reviewer: Albert Sheu (Lawrence)
Representations of quantum affine algebras in their \(R\)-matrix realization. (English) Zbl 1500.17013
Reviewer: Nenad Manojlović (Faro)
MSC:
17B37
Relation between categories of representations of the super-Yangian of a special linear Lie superalgebra and quantum loop superalgebra. (English. Russian original) Zbl 1453.81040
Theor. Math. Phys. 204, No. 3, 1227-1243 (2020); translation from Teor. Mat. Fiz. 204, No. 3, 466-484 (2020).
Isomorphism between the \(R\)-matrix and Drinfeld presentations of quantum affine algebra: types \(B\) and \(D\). (English) Zbl 1495.17024
Bannai-Ito algebras and the universal \(R\)-matrix of \(\mathfrak{osp}(1\!\!\mid\!\!2)\). (English) Zbl 1472.16030
Reviewer: Yang Shilin (Beijing)
A connection between the classical r-matrix formalism and covariant Hamiltonian field theory. (English) Zbl 1451.81253
Affine quantum super Schur-Weyl duality. (English) Zbl 1432.14018
Reviewer: Dmitry Artamonov (Moskva)
Set-theoretical solutions to the reflection equation associated to the quantum affine algebra of type \(A^{(1)}_{n-1}\). (English) Zbl 1481.37084
KZ equations and Bethe subalgebras in generalized Yangians related to compatible \(R\)-matrices. (English) Zbl 1482.81020
General mathematical formulation of scattering processes in atom-diatomic collisions in the RmatReact methodology. (English) Zbl 1462.92061
Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 377, No. 2154, Article ID 20180409, 20 p. (2019).
MSC:
92E20
A universal construction of Calogero-Moser system with two types spins interaction. (English) Zbl 1452.81129
A cluster realization of \(U_q(\mathfrak {sl}_{\mathfrak {n}})\) from quantum character varieties. (English) Zbl 1451.17006
Reviewer: Volodymyr Mazorchuk (Uppsala)
Braided Yangians. (English) Zbl 1414.81136
Equivalences between three presentations of orthogonal and symplectic Yangians. (English) Zbl 1472.17051
On the elliptic \(\mathfrak{gl}_2\) solid-on-solid model: functional relations and determinants. (English) Zbl 1477.81050
Reviewer: Norbert Hounkonnou (Cotonou)
Towards formalization of the soliton counting technique for the Khovanov-Rozansky invariants in the deformed \(\mathcal{R}\)-matrix approach. (English) Zbl 1407.81006
Reviewer: J. N. Alonso Alvarez (Vigo)
Cluster realization of \(\mathcal{U}_q(\mathfrak{g})\) and factorizations of the universal \(R\)-matrix. (English) Zbl 1456.17011
Reviewer: Volodymyr Mazorchuk (Uppsala)
Stokes phenomenon, Gelfand-Zeitlin systems and relative Ginzburg-Weinstein linearization. (English) Zbl 1401.53072
Reviewer: Akira Asada (Takarazuka)
A uniform realization of the combinatorial \(R\)-matrix for column shape Kirillov-Reshetikhin crystals. (English) Zbl 1392.05115
Affinizations and R-matrices for quiver Hecke algebras. (English) Zbl 1475.16024
Reviewer: Chun-Ju Lai (Taipei)
Generalized Yangians and their Poisson counterparts. (English. Russian original) Zbl 1382.81120
Theor. Math. Phys. 192, No. 3, 1243-1257 (2017); translation from Teor. Mat. Fiz. 192, No. 3, 351-368 (2017).
Geometric interpretation of Zhou’s explicit formula for the Witten-Kontsevich tau function. (English) Zbl 1381.37088
Reviewer: Amin Gholampour (College Park)
On the origin of dual Lax pairs and their \(r\)-matrix structure. (English) Zbl 1379.37117
Reviewer: Arsen Melikyan (Brasília)
Center of the quantum affine vertex algebra associated with trigonometric \(R\)-matrix. (English) Zbl 1428.17018
Maximally extended \(\mathfrak{sl}(2|2)\), \(q\)-deformed \(\mathfrak{d}(2,1;\epsilon)\) and 3D kappa-Poincaré. (English) Zbl 1371.81175
Meromorphic tensor equivalence for Yangians and quantum loop algebras. (English) Zbl 1432.17012
Reviewer: Volodymyr Mazorchuk (Uppsala)
Multispecies totally asymmetric zero range process. I. Multiline process and combinatorial \(R\). (English) Zbl 1400.37096
Higher-order analogues of the unitarity condition for quantum \(R\)-matrices. (English. Russian original) Zbl 1359.16037
Theor. Math. Phys. 189, No. 2, 1554-1562 (2016); translation from Teor. Mat. Fiz. 189, No. 2, 176-185 (2016).
“Twisted” rational \(r\)-matrices and the algebraic Bethe ansatz: applications to generalized Gaudin models, Bose-Hubbard dimers, and Jaynes-Cummings-Dicke-type models. (English. Russian original) Zbl 1357.82015
Theor. Math. Phys. 189, No. 1, 1509-1527 (2016); translation from Teor. Mat. Fiz. 189, No. 1, 125-146 (2016).
Maximally extended \({\mathfrak{sl}}(2|2)\) as a quantum double. (English) Zbl 1357.81118
Reviewer: Jan E. Grabowski (Lancaster)
Toric networks, geometric \(R\)-matrices and generalized discrete Toda lattices. (English) Zbl 1352.37163
\(\mathrm{SU}(2)/\mathrm{SL}(2)\) knot invariants and Kontsevich-Soibelman monodromies. (English. Russian original) Zbl 1346.81073
Theor. Math. Phys. 187, No. 2, 678-694 (2016); translation from Teor. Mat. Fiz. 187, No. 2, 263-282 (2016).
The \(q\)-commutators of braided groups. (Chinese. English summary) Zbl 1349.17017
Near invariance of the hypercube. (English) Zbl 1350.15017
Reviewer: Francisco Marcellán (Leganes)
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